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By Edited by: Bostjan Polajzer
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Extra resources for Magnetic Bearings, Theory and Applications
Example text
Where Fe K ki 2 K ks 2K p2 p3 (11) I 02 , (12) I0 , (13) I 02 , (14) D02 D02 D03 3 , 2 D0 4 2 D02 . (15) (16) For zero-power control system, the control current of the electromagnet is converged to zero to satisfy the following equilibrium condition Fe mg , (17) and the equation of motion of the suspension system can be written as mx F mg . ) . (19) From Eqs. (11), (17) and (18), This is the fundamental equation for describing the motion of the suspended object. 3 Design of Zero-Power Controller Negative stiffness is generated by actively controlled zero-power magnetic suspension.
The general expression for compliance of a system presented in Eq. (1) is given by Compliance x F 1 2 2 (k m ) (c ) 2 . (2) The compliance in Eq. (2) can be represented as Compliance x F 1/ k 2 2 (1 ( / n ) ) 4 2 ( / n ) 2 , (3) where n : the natural frequency of the system and : the damping ratio. 3 Transmissibility Transmissibility is defined as the ratio of the dynamic output to the dynamic input, or in other words, the ratio of the amplitude of the transmitted vibration (or transmitted force) to that of the forcing vibration (or exciting force).
Discretization of the model (a), and refined mesh in the air gap with integration contour for radial force computation (b) Linearization of radial force characteristic of active magnetic bearings using finite element method and differential evolution 31 b) a) Fig. 5. 3 Impact of magnetic non-linearities on radial force characteristic The flux density plot and the equipotential plot is given in Figs. 5 and 6 for a heavy load condition in the y axis (ix = 0 A, iy = 3 A) at the rotor central position (x = y = 0).